YES

Problem:
 minus(x,0()) -> x
 minus(s(x),s(y)) -> minus(x,y)
 quot(0(),s(y)) -> 0()
 quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
 plus(0(),y) -> y
 plus(s(x),y) -> s(plus(x,y))
 plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))

Proof:
 DP Processor:
  DPs:
   minus#(s(x),s(y)) -> minus#(x,y)
   quot#(s(x),s(y)) -> minus#(x,y)
   quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
   plus#(s(x),y) -> plus#(x,y)
   plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0())))
  TRS:
   minus(x,0()) -> x
   minus(s(x),s(y)) -> minus(x,y)
   quot(0(),s(y)) -> 0()
   quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
   plus(0(),y) -> y
   plus(s(x),y) -> s(plus(x,y))
   plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
  EDG Processor:
   DPs:
    minus#(s(x),s(y)) -> minus#(x,y)
    quot#(s(x),s(y)) -> minus#(x,y)
    quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
    plus#(s(x),y) -> plus#(x,y)
    plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0())))
   TRS:
    minus(x,0()) -> x
    minus(s(x),s(y)) -> minus(x,y)
    quot(0(),s(y)) -> 0()
    quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
    plus(0(),y) -> y
    plus(s(x),y) -> s(plus(x,y))
    plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
   graph:
    plus#(s(x),y) -> plus#(x,y) -> plus#(s(x),y) -> plus#(x,y)
    plus#(s(x),y) -> plus#(x,y) ->
    plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0())))
    plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0()))) ->
    plus#(s(x),y) -> plus#(x,y)
    plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0()))) ->
    plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0())))
    quot#(s(x),s(y)) -> quot#(minus(x,y),s(y)) ->
    quot#(s(x),s(y)) -> minus#(x,y)
    quot#(s(x),s(y)) -> quot#(minus(x,y),s(y)) ->
    quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
    quot#(s(x),s(y)) -> minus#(x,y) ->
    minus#(s(x),s(y)) -> minus#(x,y)
    minus#(s(x),s(y)) -> minus#(x,y) -> minus#(s(x),s(y)) -> minus#(x,y)
   SCC Processor:
    #sccs: 3
    #rules: 4
    #arcs: 8/25
    DPs:
     quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
    TRS:
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     quot(0(),s(y)) -> 0()
     quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
     plus(0(),y) -> y
     plus(s(x),y) -> s(plus(x,y))
     plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [quot#](x0, x1) = x0,
      
      [plus](x0, x1) = x0 + x1,
      
      [quot](x0, x1) = x0,
      
      [s](x0) = x0 + 1,
      
      [minus](x0, x1) = x0,
      
      [0] = 0
     orientation:
      quot#(s(x),s(y)) = x + 1 >= x = quot#(minus(x,y),s(y))
      
      minus(x,0()) = x >= x = x
      
      minus(s(x),s(y)) = x + 1 >= x = minus(x,y)
      
      quot(0(),s(y)) = 0 >= 0 = 0()
      
      quot(s(x),s(y)) = x + 1 >= x + 1 = s(quot(minus(x,y),s(y)))
      
      plus(0(),y) = y >= y = y
      
      plus(s(x),y) = x + y + 1 >= x + y + 1 = s(plus(x,y))
      
      plus(minus(x,s(0())),minus(y,s(s(z)))) = x + y >= x + y = plus(minus(y,s(s(z))),minus(x,s(0())))
     problem:
      DPs:
       
      TRS:
       minus(x,0()) -> x
       minus(s(x),s(y)) -> minus(x,y)
       quot(0(),s(y)) -> 0()
       quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
       plus(0(),y) -> y
       plus(s(x),y) -> s(plus(x,y))
       plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
     Qed
    
    DPs:
     minus#(s(x),s(y)) -> minus#(x,y)
    TRS:
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     quot(0(),s(y)) -> 0()
     quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
     plus(0(),y) -> y
     plus(s(x),y) -> s(plus(x,y))
     plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
    Subterm Criterion Processor:
     simple projection:
      pi(minus#) = 1
     problem:
      DPs:
       
      TRS:
       minus(x,0()) -> x
       minus(s(x),s(y)) -> minus(x,y)
       quot(0(),s(y)) -> 0()
       quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
       plus(0(),y) -> y
       plus(s(x),y) -> s(plus(x,y))
       plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
     Qed
    
    DPs:
     plus#(s(x),y) -> plus#(x,y)
     plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0())))
    TRS:
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     quot(0(),s(y)) -> 0()
     quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
     plus(0(),y) -> y
     plus(s(x),y) -> s(plus(x,y))
     plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [plus#](x0, x1) = x0 + x1,
      
      [plus](x0, x1) = x0 + x1 + 1,
      
      [quot](x0, x1) = x0 + x1,
      
      [s](x0) = x0 + 1,
      
      [minus](x0, x1) = x0,
      
      [0] = 0
     orientation:
      plus#(s(x),y) = x + y + 1 >= x + y = plus#(x,y)
      
      plus#(minus(x,s(0())),minus(y,s(s(z)))) = x + y >= x + y = plus#(minus(y,s(s(z))),minus(x,s(0())))
      
      minus(x,0()) = x >= x = x
      
      minus(s(x),s(y)) = x + 1 >= x = minus(x,y)
      
      quot(0(),s(y)) = y + 1 >= 0 = 0()
      
      quot(s(x),s(y)) = x + y + 2 >= x + y + 2 = s(quot(minus(x,y),s(y)))
      
      plus(0(),y) = y + 1 >= y = y
      
      plus(s(x),y) = x + y + 2 >= x + y + 2 = s(plus(x,y))
      
      plus(minus(x,s(0())),minus(y,s(s(z)))) = x + y + 1 >= x + y + 1 = plus(minus(y,s(s(z))),minus(x,s(0())))
     problem:
      DPs:
       plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0())))
      TRS:
       minus(x,0()) -> x
       minus(s(x),s(y)) -> minus(x,y)
       quot(0(),s(y)) -> 0()
       quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
       plus(0(),y) -> y
       plus(s(x),y) -> s(plus(x,y))
       plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
     Usable Rule Processor:
      DPs:
       plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0())))
      TRS:
       minus(s(x),s(y)) -> minus(x,y)
       minus(x,0()) -> x
      Bounds Processor:
       bound: 1
       enrichment: match-dp
       automaton:
        final states: {5}
        transitions:
         plus{#,0}(10,7) -> 5*
         minus0(3,1) -> 7,3
         minus0(3,3) -> 3*
         minus0(4,6) -> 7*
         minus0(1,2) -> 3*
         minus0(1,8) -> 10*
         minus0(2,1) -> 7,3
         minus0(2,3) -> 3*
         minus0(3,2) -> 3*
         minus0(3,4) -> 10*
         minus0(3,8) -> 10*
         minus0(4,9) -> 10*
         minus0(1,1) -> 7,3
         minus0(1,3) -> 3*
         minus0(2,2) -> 3*
         minus0(2,8) -> 10*
         s0(2) -> 2*
         s0(4) -> 8*
         s0(1) -> 6,2
         s0(8) -> 9*
         s0(3) -> 2*
         00() -> 1*
         plus{#,1}(22,19) -> 5*
         minus1(2,20) -> 22*
         minus1(3,3) -> 22*
         minus1(3,17) -> 19*
         minus1(3,21) -> 22*
         minus1(1,18) -> 19*
         minus1(1,20) -> 22*
         minus1(2,17) -> 19*
         minus1(3,18) -> 19*
         minus1(3,20) -> 22*
         minus1(1,17) -> 19*
         s1(20) -> 21*
         s1(17) -> 18*
         s1(2) -> 20*
         s1(1) -> 20*
         s1(3) -> 20*
         01() -> 17*
         1 -> 19,7,3,4
         2 -> 19,7,3,4
         3 -> 22,19,10,7,4
       problem:
        DPs:
         
        TRS:
         minus(s(x),s(y)) -> minus(x,y)
         minus(x,0()) -> x
       Qed